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hw5 - S09 - Chemical Engineering 150A Spring Semester 2009...

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Chemical Engineering 150A Spring Semester, 2009 Homework 5: Macroscopic Balances, Open Channels, and Compressible Flows Problem 1 Water flow in open channels can be controlled and measured by a sluice gate, shown schematically in the figure below. At a moderate distance upstream and downstream of the gate (sections 1 and 2), the flow is uniform and the pressure distribution is hydrostatic. Derive an equation relating the force F required to hold the gate as a function of the density ρ , the upstream velocity V 1 , the channel width (into the page) b, and the upstream and downstream channel heights h 1 and h 2 . Neglect bottom friction in your analysis. Problem 2 Problem 6.6 in Process Fluid Mechanics Problem 3 A pump delivers water at a steady rate of 20 L/s. Just upstream of the pump where the pipe diameter is 9.0 cm, the pressure is 125 kPa and the temperature is 298.3 K. Just downstream of the pump where the pipe diameter is 2.5 cm, the pressure is 400 kPa and the temperature is 298.2 K. Heat is lost through the pump at a rate of 5 kW. The change in elevation across the
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